Chapter 3: Scientific Measurement

1. Chapter 3: Scientific Measurement A. Types of Measurements: • Quantitative – number and unit – counting or measuring • Qualitative – observations using the 5 senses - distinctive characteristics determine the specific make-up of a substance • In chemistry, we use both quantitative and qualitative types of analysis

2. B. Scientific Notation: • Used to shorten really long numbers • General form: _ . _ x 10exp • Positive exponent: # > 1 (greater than) • Negative exponent: # 0-1 (decimal) • Only when there is a negative sign in front of the first set of numbers is the number negative (a neg. exp. does not mean a neg. #!) ex. 3.6 x 103 is a pos. # > 1 3.6 x 10-3 is a pos. # < 1 (but > 0) -3.6 x 103 is a neg. #

3. Why use scientific notation? ex. 3.6 x 103 = 3600. (decimal moves right) 3.6 x 10-3 = .0036 (decimal moves left) -3.6 x 103 = -3600 6.02 x 1023 = whoa mama! 602000000000000000000000 (21 0’s) • Practice these: • ex. 3.17 x 107 = • 6.1 x 10-5 = • 1800000 = • 0.000482 = 31700000 0.000061 1.8 x 106 4.82 x 10-4

4. How do you plug scientific notation into the calculator for calculations? • Hit open parenthesis button “(” • Type in the decimal part “_ . _” • Hit the exponent button “EXP” or “EE” (this button means “x 10”) - no need to type “x 10” • Type in the exponent part “#” • Hit the close parenthesis button “)” • Hit the operations button (+, -, x, ÷)

5. How to read the answer on the calculator? • Enter “3.62171 x 10-14” into the calculator • 3.62171E-14 = 3.6 x 10-14 • 3.62171 x10-14 = 3.6 x 10-14 • 3.62171 -14 = 3.6 x 10-14 • Practice these: • ex. (3.0 x 104) x (2.0 x 102) = • (8.0 x 109) ÷ (2.0 x 104) = • (3.6 x 1013) / (1.4 x 10-3) = • (7.481 x 10-5) x (4.2 x 10-2) = 6.0 x 106 4.0 x 105 2.6 x 1016 3.1 x 10-6

6. C. Significant Figures: • Significant figures (sig figs) – are the “important numbers” in a # • Rules for rounding answers: • Answers should be reported according to the least amount of decimal places in the data ex. (7.481 x 10-5) x (4.2 x 10-2) = 3.1 x 10-6 3 decimals 1 decimal 1 decimal

7. Rounding to a decimal place: • When you have more numbers in your calculator as an answer and you have to round to the correct number of sig figs: • Look at the decimal place to the right of the last sig fig that you need to report • If the number is 5-9, you round up • If the number is 0-4, you round down (last number stays the same) ex. 726.835 to 2 decimals = 24.8514 to 3 decimals = 726.84 24.851

8. Rules to determine sig figs from numbers: • Every non-zero digit in a measurement is significant (ex. 24.7, 0.743, 714) • Zeros between non-zeros are significant (ex. 7003, 40.79, 1.503) • Zeros to the left of non-zeros are notsignificant (ex. 0.0071, 0.42, 0.000099)

9. Rules (cont.): • Zeros at the end of a number (right of the decimal) are significant (ex. 43.00, 1.010) • Zeros at the end of a number (left of the “understood – not written” decimal) are notsignificant (ex. 300, 7000, 27210) • Zeros at the end of a number (left of the decimal) are significant (ex. 300., 27210.)

10. Sig figs in measurements: • Write down all known numbers, plus one extra number that is estimated ex. (a) 0.6 m = 60 cm = 600 mm (b) 0.61 m = 61 cm = 610 mm (c) 0.607 m = 60.7 cm = 607 mm

11. Precision vs. accuracy: • Precision – how close measurements are to each other (repeated trials) • Accuracy – how close measurements are to the actual or accepted value ex. Precise but not accurate Both precise and accurate Not accurate and not precise

12. Percent error: • Experimental (e) – your value obtained • Accepted (a) – the correct or true value • | | = absolute value (make value positive) • Formula: | accepted – experimental | x 100 accepted Shorthand: | a – e | x 100 a Answer: _____ %

13. D. Types Of Measurements: • SI units: • SI - International System of Units (standard measurements in science) • Uses the metric system (based on 10) • Time = seconds (s) • Temperature = Kelvin (K) • Length = meter (m) • Mass = kilogram (kg) • Volume = cubic meter (m3)

14. Prefixes used: • Prefixes go in front of the unit symbol and are always lower case • Kilo (k) = 1000 or 103 (1000 times larger) • Centi (c) = 0.01 or 10-2 (100 times smaller) • Milli (m) = 0.001 or 10-3 (1000 times smaller)

15. Length: • Units: • Meter (m) – SI unit • Centimeter (cm) • Millimeter (mm) • Use a meter stick or ruler (cm side only) • Conversions: • 1 m = 100 cm = 1000 mm • 1 km = 1000 m

16. Mass: • Weight – the force on an object by gravity – is different on the earth and moon • Mass – the amount of matter (“stuff”) in an object – is the same with or without gravity (the same on the earth and moon) • Use a digital balance in lab

17. Mass (cont.): • Units: • Kilogram (kg) – SI unit • Gram (g) • Milligram (mg) • Conversions: • 1 kg = 1000 g • 1 g = 1000 mg

18. Volume: • Regular shaped solid: • Measure using a meter stick or a cm ruler • V = L x W x H • Units: cm x cm x cm = cm3 • Irregular shaped solid: • Measure using the displacement method (use graduated cylinder and water) • Units: mL or L

19. Volume (cont.) • Liquid: • Measure using a graduated cylinder at the meniscus (the bottom of the curve) • Units: mL or L • Units: • Liter (L) • Milliliter (mL) • Cubic centimeter (cm3) or (cc) • Conversions: • 1 L = 1000 mL • 1 mL = 1 cm3 = 1 cc

20. Density: • Density = mass / volume • D = m / V • Mass is in grams • Volume is either in cm3 or mL • Density of water (pure H2O) = 1.0 g/mL • 1 g H2O = 1 mL H2O • Object floats in H2O if D < 1.0 g/mL • Object sinks in H2O if D > 1.0 g/mL

21. Temperature: • Scales: • Fahrenheit (F) – not used in science! • Celsius (C) • Kelvin (K) – SI unit • Only Celsius (used most of the time, especially in lab) and Kelvin are used! • Use a thermometer in lab